To make the relish, preheat grill. Remove husks from corn and brush kernels with oil. Grill until kernels are tender and slightly charred, turning corn several times during grilling. Let cool and slice off the kernels into a bowl.

Conversely, slice off raw corn kernels and sauté in some oil in a skillet over medium heat until tender. Place remaining relish ingredients in the bowl and toss. Serve crab cakes with corn salsa.